TaoBRGNRegularizationType#

The regularization added in the TAOBRGN solver.

Synopsis#

typedef enum {
  TAOBRGN_REGULARIZATION_USER,
  TAOBRGN_REGULARIZATION_L2PROX,
  TAOBRGN_REGULARIZATION_L2PURE,
  TAOBRGN_REGULARIZATION_L1DICT,
  TAOBRGN_REGULARIZATION_LM,
} TaoBRGNRegularizationType;

Values#

TAOBRGN_REGULARIZATION_USER - A user-defined regularizer
TAOBRGN_REGULARIZATION_L2PROX - \(\tfrac{1}{2}\|x - x_k\|_2^\), where \(x_k\) is the latest solution
TAOBRGN_REGULARIZATION_L2PURE - \(\tfrac{1}{2}\|x\|_2^2\)
TAOBRGN_REGULARIZATION_L1DICT - \(\|D x\|_1\), where \(D\) is a dictionary matrix
TAOBRGN_REGULARIZATION_LM - Levenberg-Marquardt, \(\tfrac{1}{2} x^T \mathrm{diag}(J^T J) x\), where \(J\) is the Jacobian of the least-squares residual

Options database Key#

-tao_brgn_regularization_type <user,l2prox,l2pure,l1dict,lm> - one of the above regularization types

Notes#

If TAOBRGN_REGULARIZATION_USER, the regularizer is set either by calling TaoBRGNSetRegularizerObjectiveAndGradientRoutine() and TaoBRGNSetRegulazerHessianRoutine() or by calling TaoBRGNSetRegularizerTerm().

If TAOBRGN_REGULARIZATION_L1DICT, the dictionary matrix is set with TaoBRGNSetDictionaryMatrix() and the smoothing parameter of the approximate \(\ell_1\) norm is set with TaoBRGNSetL1SmoothEpsilon().

If TAOBRGN_REGULARIZATION_LM, the diagonal damping vector \(\mathrm{diag}(J^T J)\) can be obtained with TaoBRGNGetDampingVector().